computing partial frequencies

[Richard Brekne]

Conklin gives the following:

I (sub n) = (600/ln2)ln[1+(n^2 pi^2 Ed(sub c)^2)/ (64L^4 f^2 p(sub c) F] cents

here..
    n = partial number
    E= Youngs Modulus
    d (sub c)= diameter of plain string or core of wrapped string
    L=speaking length
    f=frequency in Hz
    p(sub c) = density of plain string or of core wire of a wrapped string
    F= loading factor for a wrapped string (= 1 for a plain string)

and of course I (sub n) is the Inharmonicity of the nth note.

Alternatively he also gives an approximation formular

I (sub n) ~ bn^2, where b 0 (600/ln2) (pi^2 Ed(sub c)^2) / (64L^4 f^2 p(sub
c)F)

He notes that stiffness due to wrapping is ignored in both of these.

Hope this is of use to you. At the end of his article series "Design and tone
in the mechanoacoustic piano" you will find a load of such formular and
definitions.


Ron Nossaman wrote:

> I may have this somewhere and either can't find it, or don't recognize it,
> but at the risk of asking yet another annoying favor...
>
> I'd like formulas for computing partials frequencies from physical string
> measurements (diameter, length, tension, freq, whatever), for plain and
> wound strings. If anyone has such a beastie handy, and wouldn't mind
> sharing, I'd appreciate it.
>
> Thanks,
> Ron N

--
Richard Brekne
I.C.P.T.G.  N.P.T.F.
Associate, PTG
Bergen, Norway